Agreed on the RIAA correction, but you dont need to buy a preamp, if you have a decent quality older stereo with PHONO inputs. That PHONO input /IS/ already setup for the RIAA. Just plug the turntable into the stereo, then connect a cord to the PREAMP OUT or TAPE OUT line on the srereo and run it to your computer sound card. You may need some adaptors to go from a RCA cable to the computer (Radio Shack has them).
I have never recorded a vinyl LP, but I know quite a lot about audio equipment. I have used Total Recorder software with Windows to record other stuff, such as a micophone, and recording the sound off video tracks. T R is decent and cheap software and runs on almost any version of Windows from Win98 and up. (Maybe some never versions wont work on older Windows)??? (I'm using an older version, which is simple).
This thread did bring up a question for me. Does NEW stereo equipment come with a PHONO input? (I bet not). I have not boughten stereo equipment in at least 25 years. I like the old stuff, and on my main stereo system, I have been using an actual power amp made for use on a stage, such as a sound system for a Rock band, and have speakers to match. More power than I'll ever need in a house, but reserve power means no distortion.